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Nth root algorithm

Index Nth root algorithm

The principal ''n''th root \sqrt of a positive real number A, is the positive real solution of the equation (for integer n there are n distinct complex solutions to this equation if A > 0, but only one is positive and real). [1]

9 relations: Complex number, Exponentiation, Limit of a sequence, Newton's method, Nth root, Principal branch, Real number, Recurrence relation, Sign (mathematics).

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

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Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

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Principal branch

In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

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Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.

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Redirects here:

N-th root algorithm, Nth-root algorithm.

References

[1] https://en.wikipedia.org/wiki/Nth_root_algorithm

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